Editing Radial stress

{{Short description|Stress in a direction radial to the axis of symmetry}}
{{more citations needed|date=December 2009}}

'''Radial stress''' is [[Stress (mechanics)|stress]] toward or away from the central [[axis of rotation|axis]] of a component.

==Pressure vessels==
The walls of [[pressure vessel]]s generally undergo triaxial loading. For cylindrical pressure vessels, the normal loads on a wall element are longitudinal stress, circumferential (hoop) stress and radial stress.

The radial stress for a thick-walled [[cylinder (engine)|cylinder]] is equal and opposite to the [[gauge pressure]] on the inside surface, and zero on the outside surface. The circumferential stress and longitudinal stresses are usually much larger for pressure vessels, and so for thin-walled instances, radial stress is usually neglected.

==Formula==
The radial stress for a thick walled pipe at a point <math>r</math> from the central axis is given by
:<math> \sigma_r(r) = \frac{p_i r_i^2 - p_o r_o^2}{r_o^2 - r_i^2}+\frac{r_i^2 r_o^2 (p_o - p_i)}{r^2 (r_o^2 - r_i^2)}\ </math>
 
where <math> r_i </math> is the inner radius, <math> r_o </math> is the outer radius, <math> p_i </math> is the inner absolute pressure and <math> p_o </math> is the outer absolute pressure.<ref>{{cite web|url=http://www.engineeringtoolbox.com/stress-thick-walled-tube-d_949.html|publisher=EngineeringToolbox|accessdate=2012-05-18|title=Stress in Thick-Walled Tubes or Cylinders 
}}</ref>  Maximum radial stress occurs when <math>r = r_i</math> (at the inside surface) and is equal to gauge pressure, or <math>p_i - p_o</math>.<ref>{{cite book|title=Mechanics of solids and structures |last1=Benham |first1=P.P. |last2=Warnock|first2=F.V. |chapter=14.4 Stress distribution in a thick-walled cylinder |pages=331-338 |edition= |date=1973 |publisher=Pitman Paperbacks |location=Bath, UK |isbn=0 273 36191 0 }}</ref>

==References==
{{Reflist}}

{{DEFAULTSORT:Radial Stress}}
[[Category:Solid mechanics]]


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